The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer (776127), страница 27
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For example, a football-shaped body, somewhere between a cylinder and sphere,may be assigned w = 1.5, and a short cylinder with a large diameter-to-height ratio may have w = 0.5.For the case where the temperature T0 > Tf is imposed on the boundary at t = 0, the melt time, tm canbe estimated bytm =L21 + 0.25 + 0.17w 0.7 Ste l2a l (1 + w ) Ste l[ ()](4.4.77)valid for 0 £ Stel £ 4.If the heat input is convective, with a heat transfer coefficient h from a fluid at temperature Ta, theapproximate melt time is© 1999 by CRC Press LLC4-116Section 4tm =L22a l (1 + w ) Ste lé 2 klù0.7êë1 + h L + 0.25 + 0.17w Ste l úû()(4.4.78)valid for 0 £ Stel £ 4 and h L / kl ³ 0.1, and the temperature, T(0,t), of the surface across which the heatis supplied can be estimated from the implicit time-temperature relationship:t=1.832ùæ T (0, t ) - Tf öæ Ta - Tf ör cl k l éê- 1ú1.18Ste+lçç÷÷22h Ste l êúè Ta - T (0, t ) øè Ta - T (0, t ) øëû(4.4.79)Both equations (4.4.78) and (4.4.79) are claimed to be accurate within 10%.The suitability of using several simplified analytical solutions for the estimation of freezing andmelting times for more-realistic problems was assessed by Dilley and Lior (1986).Defining TermsEutectic concentration: A concentration of a component of a multicomponent liquid at which theliquid would upon freezing form a solid containing the same concentration, and at which thefreezing process is completed at a single temperature.Mushy zone: The zone composed of both liquid and solid, bounded by the liquidus and solidus curves,in a freezing or melting process.ReferencesAlexiades, V.
and Solomon, A.D. 1993. Mathematical Modeling of Melting and Freezing Processes,Hemisphere Publishing, Washington, D.C.ASHRAE (American Society of Heating, Refrigerating, and Air-Conditioning Engineers). 1993. Coolingand freezing times of foods, in Fundamentals, ASHRAE, Atlanta, GA, chap.
29.ASHRAE (American Society of Heating, Refrigerating, and Air-Conditioning Engineers). 1990. Refrigeration, ASHRAE, Atlanta, GA.Cheng, K.C. and Seki, N., Eds. 1991. Freezing and Melting Heat Transfer in Engineering, HemispherePublishing, Washington, D.C.Cleland, D.J., Cleland, A.C., and Earle, R.L. 1987. Prediction of freezing and thawing times for multidimensional shapes by simple formulae: Part 1, regular shapes; Part 2, irregular shapes. Int. J.Refrig., 10, 156–166; 234–240.DeWinter, F. 1990.
Energy storage of solar systems; in Solar Collectors, Energy Storage, and Materials,MIT Press, Cambridge, MA, Section II.Dilley, J.F. and Lior, N. 1986. The evaluation of simple analytical solutions for the prediction of freezeup time, freezing, and melting. Proc. 8th International Heat Transfer Conf., 4, 1727–1732, SanFrancisco.Flemings, M.C. 1974. Solidification Processes, McGraw-Hill, New York.Fukusako, S. and Seki, N. 1987. Fundamental aspects of analytical and numerical methods on freezingand melting heat-transfer problems, in Annual Review of Numerical Fluid Mechanics and HeatTransfer, Vol. 1, T.C.
Chawla, Ed., Hemisphere, Publishing, Washington, D.C., chap. 7, 351–402.Goodman, T.R. 1964. Application of integral methods to transient nonlinear heat transfer, in Advancesin Heat Transfer, Vol. 1, T.F. Irvine and J.P. Hartnett, Eds., Academic Press, San Diego, 51–122.Hayashi, Y. and Kunimine, K.
1992. Solidification of mixtures with supercooling, in Heat and MassTransfer in Materials Processing, I. Tanasawa and N. Lior, Eds., Hemisphere Publishing, NewYork, 265–277.© 1999 by CRC Press LLCHeat and Mass Transfer4-117Incropera, F.P. and Viskanta, R. 1992. Effects of convection on the solidification of binary mixtures, inHeat and Mass Transfer in Materials Processing, I. Tanasawa and N Lior, Eds., HemispherePublishing, New York, 295–312.Lunardini, V.J. 1981. Heat Transfer in Cold Climate, Van Nostrand-Reinhold, Princeton, NJ.Poulikakos, D. 1994.
Conduction Heat Transfer, Prentice-Hall, Englewood Cliffs, NJ.Rubinsky, B. and Eto, T.K. 1990. Heat transfer during freezing of biological materials, in Annual Reviewof Heat Transfer, Vol. 3, C.L. Tien, Eds., Hemisphere Publishing, Washington, D.C., chap. 1, 1–38.Tanasawa, I. and Lior, N., Ed. 1992. Heat and Mass Transfer in Materials Processing, HemispherePublishing, New York.Yao, L.S. and Prusa, J. 1989. Melting and freezing, in Advances in Heat Transfer, Vol. 19, J.P. Hartnettand T.F.
Irvine, Eds., Academic Press, San Diego, 1–95.Further InformationMany textbooks on heat transfer (some listed in the References section above) contain material aboutmelting and freezing, and many technical journals contain articles about this subject. Some of the majorjournals, classified by orientation, areGeneral: ASME Journal of Heat Transfer, International Journal of Heat & Mass Transfer, NumericalHeat Transfer, Canadian Journal of Chemical Engineering, AIChE JournalRefrigeration: Transactions of the ASHRAE, International Journal of Refrigeration, Referigeration,Journal of Food Science, Bulletin of the International Institute of RefrigerationManufacturing: ASME Journal of Engineering for Industry, Journal of Crystal Growth, MaterialsScience and Engineering AGeophysical, climate, cold regions engineering: Limnology and Oceanography, Journal of Geophysical Research, ASCE Journal of Cold Regions Engineering, Cold Regions Science andTechnologyMedical: Cryobiology, ASME Journal of Biomechanical Engineering, Journal of General Physiology© 1999 by CRC Press LLC4-118Section 44.5 Heat ExchangersRamesh K.
Shah and Kenneth J. BellThe two major categories of heat exchangers are shell-and-tube exchangers and compact exchangers.Basic constructions of gas-to-gas compact heat exchangers are plate-fin, tube-fin and all prime surfacerecuperators (including polymer film and laminar flow exchangers), and compact regenerators. Basicconstructions of liquid-to-liquid and liquid-to-phase-change compact heat exchangers are gasketed andwelded plate-and-frame, welded stacked plate (without frames), spiral plate, printed circuit, and dimpleplate heat exchangers.Shell-and-tube exchangers are custom designed for virtually any capacity and operating condition,from high vacuums to ultrahigh pressures, from cryogenics to high temperatures, and for any temperatureand pressure differences between the fluids, limited only by the materials of construction.
They can bedesigned for special operating conditions: vibration, heavy fouling, highly viscous fluids, erosion,corrosion, toxicity, radioactivity, multicomponent mixtures, etc. They are made from a variety of metaland nonmetal materials, and in surface areas from less than 0.1 to 100,000 m2 (1 to over 1,000,000 ft2).They have generally an order of magnitude less surface area per unit volume than the compact exchangers,and require considerable space, weight, support structure, and footprint.Compact heat exchangers have a large heat transfer surface area per unit volume of the exchanger,resulting in reduced space, weight, support structure and footprint, energy requirement and cost, as wellas improved process design, plant layout and processing conditions, together with low fluid inventorycompared with shell-and-tube exchangers. From the operating condition and maintenance point of view,compact heat exchangers of different constructions are used for specific applications, such as for hightemperature applications (up to about 850°C or 1550°F), high pressure applications (over 200 bars), andmoderate fouling applications.
However, applications do not involve both high temperature and pressuresimultaneously. Plate-fin exchangers are generally brazed, and the largest size currently manufacturedis 1.2 ´ 1.2 ´ 6 m (4 ´ 4 ´ 20 ft). Fouling is one of the major potential problems in many compactexchangers except for the plate heat exchangers. With a large frontal area exchanger, flow maldistributioncould be another problem. Because of short transient times, a careful design of controls is required forstartup of some compact heat exchangers compared with shell-and-tube exchangers. No industry standards or recognized practice for compact heat exchangers is yet available.This section is divided into two parts: Compact Heat Exchangers and Shell-and-Tube Exchangers,written by R. K.
Shah and K. J. Bell, respectively. In the compact heat exchangers section, the followingtopics are covered: definition and description of exchangers, heat transfer and pressure drop analyses,heat transfer and flow friction correlations, exchanger design (rating and sizing) methodology, flowmaldistribution, and fouling. In the shell-and-tube heat exchangers section, the following topics arecovered: construction features, principles of design, and an approximate design method with an example.Compact Heat ExchangersRamesh K. ShahIntroductionA heat exchanger is a device to provide for transfer of internal thermal energy (enthalpy) between twoor more fluids, between a solid surface and a fluid, or between solid particulates and a fluid, in thermalcontact without external heat and work interactions. The fluids may be single compounds or mixtures.Typical applications involve heating or cooling of a fluid stream of concern, evaporation or condensationof single or multicomponent fluid stream, and heat recovery or heat rejection from a system.
In otherapplications, the objective may be to sterilize, pasteurize, fractionate, distill, concentrate, crystallize, orcontrol process fluid. In some heat exchangers, the fluids transferring heat are in direct contact. In otherheat exchangers, heat transfer between fluids takes place through a separating wall or into and out of a© 1999 by CRC Press LLCHeat and Mass Transfer4-119wall in a transient manner. In most heat exchangers, the fluids are separated by a heat transfer surfaceand do not mix. Such exchangers are referred to as direct transfer type, or simply recuperators.Exchangers in which there is an intermittent flow of heat from the hot to cold fluid (via heat storageand heat rejection through the exchanger surface or matrix) are referred to as indirect transfer type orsimply regenerators.The heat transfer surface is a surface of the exchanger core which is in direct contact with fluids andthrough which heat is transferred by conduction in a recuperator.
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